CLICK HERE FOR A LONGER VERSION WITH EXPLANATIONS

These tools and these tools only may be used in RTA (click the name for a download link):

XInputPlus to use a controller/gamepad with versions that don't have built in support
Dinput for fixing mouse issues
d3d9.dll to force the game into windowed mode

Useful external tools you can use during runs:

GTA MP3 Randomizer or GTA Radio External
Windowers (dxwnd, d3dwindower, 3DAnalyze)
SKeys or NohBoard for showing keyboard inputs on recordings
100 percent checklist
Autosplitter for Livesplit (activate it in Livesplit's "Edit Splits" menu)
Load remover for Livesplit
Prio for keeping 1-core-affinity setting

Other useful tools you can use for practice and testing BUT NOT DURING RUNS:

On Mission Flag changer for 3D Era GTAs

While not a mod/fix, I'd like to put here that disabling your audio devices after launching the game in order to skip all voice lines/other effects is not allowed. This is because you're changing the hardware while the game is running (similar to other banned glitches as the "open disc tray" hardware trickery in PS1 speedruns).

Trying to launch the game with no audio devices enabled causes the game to not start and throw an error, meaning you can't normally setup the hardware in this way before the game launches (and even if it didn't screw playing the whole game with no sound :P).